Creating Space for a Topic in The Null Curriculum
Bibliographic record
Abstract
Mathematics curricula continue to become more standardized worldwide, which makes researching topics not appearing in the explicit curriculum challenging. In this chapter, we describe four lessons learned while conducting classroom-based research in Canada on a topic in the null curriculum. Despite its potential to support geometric and spatial reasoning, research in projective geometry with children was abandoned decades ago. Through our project, we learned multiple lessons while resurrecting, updating, inventing, implementing, and conducting classroom-based research within the null space of projective geometry. These lessons include: (1) locating relevant curriculum resources for a non-existent topic in the elementary-grades curriculum; (2) inventing ways to create, pilot, and use unfamiliar tasks in a classroom-based setting; (3) rationalizing the value of the topic to school district personnel, teachers, parents, and students; and (4) generating reciprocal growth in understanding amongst teachers and researchers. The insights gained offer ways to explore and justify the research, teaching, and learning of topics outside of the explicit curriculum.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".